I would scrape it first. Get as much off as possible without gouging the floor, and then sand. Otherwise you will go through a lot of sandpaper as it gums up and it will be much more difficult. Scraper blades or a razor blade in a pinch should remove most of it, and it is all about the angle of the blade.

I'm not sure about the effect of white spirit on wood and the varnish, but it will get rid of the paint (but might badly damage the wood, maybe google white spirit+wood).
Otherwise, sand the whole thing, and redo the varnish, it doesn't seem like a huge surface, should not take too long.